\begin{tabular}{l}
\text{\LARGE{Binomial Distribution}}\\
\\\hline\\
\text{Binomial distribution is the discrete probability distribution of the number of}\\
\text{successes in a sequence of a given number of independent experiments with}\\
\text{equal success probability. A single success/failure experiment is also called}\\
\text{a }\textit{Bernoulli trial}\text{.}
\\\\\hline\\
\text{\Large{Input parameters}}\\
    \begin{array}{ll}\\
    \\n & \text{number of trials}\\
    \\p & \text{probability of success in a single trial}\\
    \end{array}
\\\\\hline\\
\text{\Large{Output parameters}}\\
    \begin{array}{ll}\\
    \\\text{Expected value} & \mathbf{np}\\
    \\\text{Standard deviation} & \mathbf{\sqrt{np(1-p)}}\\
    \\\text{Variance} & \mathbf{np(1-p)}\\
    \end{array}
\\\\\hline\\
\text{\Large{Additional information}}\\
    \begin{array}{ll}\\
    \\\text{Number of successes} & \mathbf{k}\\
    \\\text{Probability mass function} & \mathbf{\left(
        \begin{array}{c}
            n \\
            k
        \end{array}
    \right){p^k}\left(1-p\right)^{n-k}}\\
    \\\text{Moment-generating function} & \mathbf{\left(1-p+pe^t\right)^n}\\
    \end{array}
\end{tabular}